Title : THE QUEUE WITH POISSON INPUT AND GENERAL SERVICE TIMES, TREATED AS A BRANCHING PROCESS,

Corporate Author : PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS

Personal Author(s) : Neuts,Marcel F.

Report Date : SEP 1966

Pagination or Media Count : 35

Abstract : The MG1 queue is treated as a sequence of branching processes, the duration of which constitutes a busy period. The first generation in each branching process consists of the customers present at the beginning of the busy period, the second generation consists of all customers, who arrive during the service time of the first generation, etc. When the queue becomes idle, the branching process becomes extinct. This approach permits a more elementary treatment of the MG1 queue, without use of Rouche's theorem. It provides a natural sequence of approximants to the distributions, which is considered, and it provides a simple derivation of the virtual waitingtime. The paper also considers two random variables of interest, which have not been considered hitherto. One is the total number of customers, served in (o,t), the other is the virtual age or the time already spent in the queue, by the customer is service at time t. A new imbedded semi-Markov process is considered, and a study is made of its asymptotic behavior. (Author)